Have you ever tried to balance a pattern? Well, if so then symmetry was probably involved. Take a look at this dilemma.

Dylan looked at the work his friend Marcus was doing in class. Marcus had decided to design and build a tepee. Like Dylan’s geodesic dome, Marcus was having a difficult time with the construction aspect of the teepee.

“What seems to be the trouble?” Dylan asked Marcus as he saw Marcus sit down frustrated next to his sticks and cloth covering.

“This thing won’t stand up. I put the sticks together. They are all the same length, then I try to put the canvas over the sticks and it doesn’t fit. I am so frustrated!” Marcus exclaimed putting his head in his hands.

Dylan looked at the sticks and then as the canvas. As soon as he looked at the canvas, he knew what was wrong with Marcus’ design.

Do you know what Dylan means? What is symmetry? How does a teepee have symmetry? What would Marcus have to do to be sure that his canvas was symmetrical?

Pay attention during this Concept and you will learn all that you need to know to solve this problem and help Marcus with his teepee.

Guidance

Sometimes, a figure will have parts that mirror themselves within one object. In this case, parts of the object match other parts of the picture. This is called
symmetry
. Take a look.

Look at this heart. It has two sides that match. The heart is symmetrical because there is symmetry in its design. This heart can be divided in half vertically where one half matches the other half.
This line that divides the heart into matching parts is called the
line of symmetry.

We can determine other lines of symmetry by looking at other objects.

Look at this cross. It has two lines of symmetry. If you look, the cross can be divided in half perfectly vertically and in half horizontally. This means that there are two lines of symmetry in the cross.

We can find symmetry all around us. There is symmetry in real – world objects that we see all the time. Look around you today and locate three different things that have lines of symmetry.

Here are some butterflies to think about.

Example A

Does the figure below have symmetry? Can it be a reflection?

Solution: Yes, this figure has symmetry and can be a reflection.

Example B

How many lines of symmetry does this figure have?

Solution: This figure has two lines of symmetry.

Example C

Do these figures have symmetry?

Solution: No, these figures do not have symmetry.

Now let's go back to the dilemma from the beginning of the Concept.

We need to answer three questions.

What is symmetry?

Symmetry is when two halves of an object match. In other words, you can divide the object into parts and the parts are congruent. A heart is a symmetrical object, so is a teepee.

How does a teepee have symmetry?

A teepee has symmetry because it can be divided in half so that one half of the teepee matches the other half.

What would Marcus have to do to be sure that his canvas was symmetrical?

While Marcus was sure that his sticks were all the same length that is only half of the necessary piece. Marcus also needs to be sure that the canvas is the same all the way around. If he does, then all sides will match or be symmetrical, if not then one side will be different that the other.

Guided Practice

Here is one for you to try on your own.

Does this figure have symmetry? Can it be a reflection?

Solution

Yes, you can divide this butterfly evenly so that one side can reflect the other. Therefore, it has symmetry.